User:Azizlokhandwala/sandbox/Methods of mathemagics

'''SQUARIA : Introduction Method “SQUARIA” was invented with a purpose of making math of calculating squares simple. As you know sometimes their is a situation in which you know square of number but you don't know square of other number and to find that other number we have to follow traditional or Vedic method for squaring which is sometimes quite complicated and time consuming too. So squaria is a method by which we can find square of number you want to find by using a number whose square is known to you. MULTICA : Introduction Method “MULTICA” was invented with a purpose of making math of calculating multiplication of two numbers more simple. As you know sometimes there is a situation in which you know square of number and that same number application is in some multiplication with other number. So the thing is you can find product of that two numbers using “MULTICA”. It is sometimes very because of its easy and quick application for getting answers. CUBICA: Introduction Method “CUBICA” was invented with a purpose of making math of calculating cubes simple. As you know sometimes there is a situation in which you know cube one of number but you don't know cube of other number and to find that other number you have to follow traditional or Vedic method for squaring which is sometimes quite complicated and time consuming too. SQUARIA : Method for calculating squares x2+[(x+y)(y−x)] In method “Squaria” if you know square of any one number and you want to find square of other number you can do this by Squaria by just using above formula. In this equation “x” is one number whose square is known to us and “y” is the number with which “x” is going to be multiplied. In this equation by knowing just square of one number we can find product of that number with any other number. - SQUARIA: Stepwise representation for using a table chart Knowing one square Reading question Use of Formula Replacing values Getting answer SQUARIA: Illustrations Example with two digit number: Suppose you know 2 22=484 And you have to find Using SQUARIA formula x 2 +[(x+y)(y−x)] 2 32=? So let’s see further procedure... Hold your hot coffee!!! 2 22 + [(22 + 23)(23 − 22)]  = 484 + (45 * 1)   = 484 + 45  = 529 Example with three digit number: Suppose you know 1 232=15129 1 262=? Using SQUARIA formula x 2 +[(x+y)(y−x)] So let’s see further procedure... Hold again your hot coffee!!! = 15129 + [(249)(3)]  = 15129 + 747  = 15876 And you want to find Example with four digit number: Suppose you know 4 5672=20857489 And you want to find 4 5732=? Using SQUARIA formula x 2 +[(x+y)(y−x)] So let’s see further procedure... Bored with coffee! Let’s have a Cup of Tea!!! = 20857489 + (4573 − 4567)(4573 + 4567)  = 20857489 + (6)(9140)  = 20857489 + 54840  = 20912329 According to me you may have enjoyed SQUARIA with your cup of tea and coffee :) NOTE: Do not solve brackets in formula because when you solve it you will find that it is square of other number but to find square of that other number using a square of number which we know, I have made SQUARIA. CUBICA : Method for calculating cubes x3 +[x2 +y2 +(xy)](y−x) The above equation can be said as a golden equation for our application in our life because it is the equation which can be used instead of traditional or Vedic method which are sometimes time consuming and complicated too. In “cubica”, “x” denotes number whose cube is known to us and “y” denotes number whose cube you want to find. So let’s be more clear above equation using a pictorial representation of steps necessary for getting correct answer for number whose cube you want to find. CUBICA : Stepwise representation for using a table chart Knowing one cube Reading question Use of Formula Replacing values Getting answer CUBICA : Illustrations Example with two digit number Suppose you know 2 33=12167 And you have to find 3 23=? Using CUBICA formula x 3 +[x2 +y2 +(xy)](y−x) So let’s see further procedure... Hold your cold drink! 2 33+[232+322+(23*32)](32−23) = 12167 + [529 + 1024 + 736](9)   = 12167 + 20601  = 32768 Example with three digit number Suppose you know 1 273=2048383 And you have to find 1 343=? Using CUBICA formula x 3 +[x2 +y2 +(xy)](y−x) So let’s see further procedure... Hold your cold drink again! 1 273 + [1272 + 1342 + (127 * 134)](134 − 127)  = 20483383 + [16129 + 17956 + 17018](7)   = 2048383 + 357721  = 2406104 Example with four digit number Suppose you know And you have to find 1 2743=2067798824 1 2833=? Using CUBICA formula x 3 +[x2 +y2 +(xy)](y−x) So let’s see further procedure... Hold your cold drink again! 1 2743 + [12742 + 12832 + (1274 * 1283)](1283 − 1274)   = 2067798824 + [1623076 + 16460689 + 1634542](9)   = 2067798824 + 44133363  = 2111932187 According to me you may have enjoyed CUBICA with your cold drink :) NOTE: Do not solve brackets in formula because when you solve it you will find that it is cube of other number but to find cube of that other number using a cube of number which you know, I have made CUBICA. MULTICA - I: Method for calculating Products using Squares x2 + x(y − x) [here y > x], x2 − x(y − x) [here y < x] The above equation can be said as a Platinum “ :) ” equation for our application in our life because by this equation we can find product of two numbers by using square of a number in which the number is a part of that two numbers of which we have to find product. In this equation “x” is one number whose square is known to us and “y” is the number with which “x” is going to be multiplied. In this equation by knowing just square of one number we can find product of that number with any other number. MULTICA I : Stepwise representation for using a table chart Knowing no. square Reading question Use of Formula Replacing values Getting answer MULTICA - I : Illustrations Examples of two digit number: Suppose we know 232 = 529 And we have to find 23*29 = ? Now using the formula, [x2 + x(y − x)] = 232 + 23(29 − 23) = 529 + 138 = 667 NOTE: In this 29 > 23 (i.e. y > x) and due to that we have used but if (y < x) we have to do a small change in formula like this [x2 − x(y − x)] Here is one example 242 = 576 And we have to find 24*22 = ? Now using the formula for (y < x), 576 − 24(2) = 576 − 48 = 528 Examples with three digit number: Suppose we know 1232 = 15129 And we want to find 123*127 = ? Now using formula for (y > x), [x2 + x(y − x)] = 15129 + 123(4) = 15129 + 492 = 15621 Let’s see one example with (y < x), 1242 = 15376 124*121 = ? Now using formula for (y < x), = 15376 − 124(3) = 15376 − 372 = 15004 Examples with four digit number: Suppose we know 12342 = 1522756 And we want to find 1234*1242 = ? Now using formula for (y > x), [x2 + x(y − x)] = 1522756 + 1234(8) = 1522756 + 9872 = 1532628 Let’s see one example with (y < x), 12462 = 1552516 1246*1239 = ? Now using formula for (y < x), = 1552516 − 1246(7) = 1552516 − 8722 = 1543794 NOTE:You may have observe that I am neglecting negative sign when solving for (y < x), I have done it because for this method negative sign doesn't matter. This method is applicable to any number of digits you want but sufficient condition is you should know square of one number. MULTICA - II: Method for calculating Products using Cubes [x3 + x(y − x2)] The above equation can be said as a Uranium “ :) ” equation for our application in our life because by this equation we can find product of two numbers by using cube of a number in which the number is a part of that two numbers of which we have to find product. In this equation “x” is one number whose cube is known to us and “y” is the number with which “x” is going to be multiplied. In this equation by knowing just cube of one number we can find product of that number with any other number. MULTICA II : Stepwise representation for using a table chart    Knowing no. cube Reading question Use of Formula Replacing values Getting answer MULTICA II : Illustrations Examples of two digit number: Suppose we know 223 = 10648 And we have to find 22*29 = ? Now using the formula, [x3 + x(y − x2)] = 223 + 22(29 − 484) = 10648 + 22(-455) = 10648 - 10010 = 638 Examples with three digit number: Suppose we know 1163 = 1560896 And we want to find 116*125 = ? Now using formula, [x3 + x(y − x2)] = 1560896 + 116(125-13456) = 1560896 + 116(-13331) = 1560896 - 1546396 = 14500Bold text'''